Evolution of optimal Hill coefficients in nonlinear public goods games

Marco Archetti, I. Scheuring

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

In evolutionary game theory, the effect of public goods like diffusible molecules has been modelled using linear, concave, sigmoid and step functions. The observation that biological systems are often sigmoid input–output functions, as described by the Hill equation, suggests that a sigmoid function is more realistic. The Michaelis–Menten model of enzyme kinetics, however, predicts a concave function, and while mechanistic explanations of sigmoid kinetics exist, we lack an adaptive explanation: what is the evolutionary advantage of a sigmoid benefit function? We analyse public goods games in which the shape of the benefit function can evolve, in order to determine the optimal and evolutionarily stable Hill coefficients. We find that, while the dynamics depends on whether output is controlled at the level of the individual or the population, intermediate or high Hill coefficients often evolve, leading to sigmoid input–output functions that for some parameters are so steep to resemble a step function (an on–off switch). Our results suggest that, even when the shape of the benefit function is unknown, biological public goods should be modelled using a sigmoid or step function rather than a linear or concave function.

Original languageEnglish
Pages (from-to)73-82
Number of pages10
JournalJournal of Theoretical Biology
Volume406
DOIs
Publication statusPublished - Oct 7 2016

Fingerprint

Sigmoid Colon
Game
Step function
Concave function
Coefficient
game theory
enzyme kinetics
Linear Function
Enzyme Kinetics
Evolutionary Game Theory
kinetics
Hill Equation
Game Theory
Biological Systems
Switch
Kinetics
Molecules
Enzyme kinetics
Predict
Unknown

Keywords

  • Cooperation
  • Enzyme kinetics
  • Game theory
  • Hill equation
  • Mechanism design
  • Michaelis–Menten
  • Public goods

ASJC Scopus subject areas

  • Applied Mathematics
  • Statistics and Probability
  • Modelling and Simulation
  • Agricultural and Biological Sciences(all)
  • Biochemistry, Genetics and Molecular Biology(all)
  • Immunology and Microbiology(all)
  • Medicine(all)

Cite this

Evolution of optimal Hill coefficients in nonlinear public goods games. / Archetti, Marco; Scheuring, I.

In: Journal of Theoretical Biology, Vol. 406, 07.10.2016, p. 73-82.

Research output: Contribution to journalArticle

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